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河北省邯郸市永年区实验中学2024-2025学年第一学期八年级开学摸底试卷试题(数学)试卷答案
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changenatureforourgoals-somuchthatitseemswemaybeindangerofinfluencingitseriously.“Wantmetoplayyourfavoritesong?”Kameronasked..“Ofcourse,”Gustavanswered.tInANaturalHistoryoftheFuture,biologistRobDunnthinksthatnothingcouldbefurtherwastheonlysongKameronknew.fromthetruth:ratherthanaskingwhethernaturewillletuslive,we'dbetteraskwhetherwewillThesmallviolinrestedseriouslyunderKameron'schin()Sheplayedasbestsheletnaturelast.Althoughwetryourbest,orworst,tocontrolthebiologicalworld,lifehasitsowncould.Vivianbeatherlegtokeeprhythm(forKameron.GustayheldVivian'sotherhand.laws,andnomatterwhatmandoes,hecannotchangethem.Itwasnottheperformancethatwasmoving,butthememoriesitbrought.Explainingseveralbasiclawsofecology(),Dunnshowswhylifecannotbestopped.We24.WhyisKameronspecialcomparedwithotherkids?growonesinglecroponthefield,onlytofindnewlifeappearingtoattackthem.WethrowawayA.Shelikesplayingoutside.B.Shecaresabouttheelderly.poisonous(有毒的)waste,onlytofindmicrobes(微生物)takingitover.AndevenintheLondonC.ShehasplentyofenergyD.Shecandrawonthesidewalk.Tube,wehaveseenanewtypeofmosquitoappeartotakeadvantageofaplacethatisclearlynotfit25.WhydidKameronknockonthecouple'sdoor?tolive.Lifewillnotfollowourplans.Instead,DunnshowsusthefutureoflivingthingsandtheA.Toaskforpraisebysingingasong.B.Tolearntheviolinfromthem.D.Tomakemoneybyplayingtheviolin.challengesthatthenextgenerationmayfaceC.Tocheerthemupwithmusic.ANaturalHistoryoftheFuturesetsanewstandardforunderstandingthedifferentkindsoflife26.Whatdidthecoupleusetodoeveryday?A.GoforawalkB.Makeadrive.andourfutureasakindofcreature.C.StayathomeD.Dowoodworking.Weight:478g27.Whatisthemostmovingforthecouple?Size:223×146×33mmA.Thelovebetweenthem.B.Vivian'sattitudetothemusic.Price:￡25.00C.Kameron'sperformance.D.Thinkingbacktopastexperiences.WaystoBuy:Theycanbegotinbookstoresandonline.C21.Whatdoestheauthorthinkofhumans'scientificachievements?AmericanscelebrateLaborDaythisyearonSeptember5.ThenationalholidaybeganmoreA.Theyhelphumansbeatnature.B.Theydogoodtonatureinmanyways.than100yearsagotohonorlow-paidfactoryworkersC.Theymaychangenaturetoomuch.D.Theyaredevelopedtooslowly.LaborDayalsomarkstheendofsummer.ManystudentsreturntoschoolafterLaborDay.The22.Whichofthefollowingagreeswiththeideainthebook?hotdaysofsummerturncooler.ManyAmericanscelebratetheholidaywithanoutdoorfamilyA.Livingthingslikepoisonouswaste.B.Lifewillbeoutofcontrolinthefuture.picnic.C.Lifecanliveinanylivingconditions.D.LivingthingshavetheirownrulestofollowButLaborDaystartedwithastruggle(奋斗).OnMay1,I889,workersmarched(游行)on23.Whomaybemostprobablyinterestedinthebookintroducedinthetext?thestreetsofParis,France.InternationalLaborDaywasborn.MostindustrializedcountriesintheA.Historians.B.Naturalists.C.Businessmen.D.Artists.world-excepttheUnitedStatesandCanada-celebrateLaborDayonthefirstofMay.BOnSeptember5,1882,inNewYorkCity,about10,000workerswalkedthroughthestreetstoOnaSaturdayafternoon,youfindmostkidsoutsideplayinggames.Kidsaremadefortheshowthestrengthoflabororganizations.Formanyyearsafterthat,Americanworkersusedthefirstoutdoors,withtheirendlessenergyandtheeasywayinwhichtheymakefriends.It'snotdifferentMondayinSeptembertoaskforbetterworkingconditionsandpay.MusicwasapartofmanyofforKameron,anordinary,fun-loving7-year-oldgirlwholovestodrawouttheworld'slongestthosemarches.hopscotch(跳格子)onthesidewalk.Laborsongstraditionallytellstoriesofconflictsandhopesforabetterlife.ManytraditionalAmericanlaborsongscamefromworkersinthecoalminesoftheSouth.MineownersInbetweenjump-ropegames,basketballshootoutsandskateboardraces,Kamerontakestimewereagainstworkers'unions.InKentucky,thecompanypolicesearchedforunionleaders.Theytodosomethingspecialforherelderlyneighbors.Kameron'sneighborhoodishometoagoodmixwaitedoutsideaworker'shomeforseveraldaystostophimfromorganizingmarches.Thecoalofyoungfamiliesandelderlyneighborswhosechildrenhavelongsincelefthome.Kameronfirststartedwavingtothem.Mostofthemsmiledback.miner'swife,FlorenceReece,stayedinsidewithherchildren.Shewrotethissong,"WhichSideAreYouOn?”ThenKamerondecidedthatsomeofthemneededalittlepleasure.Sosheranhome,tookherAnotherAmericanlaborsongiscalled"BreadandRoses".BasedonapoembyJamesviolinandmadetherounds."CanIplayyouasong?"sheasked,afterknockingonthedoor.Oppenheim,itwaspublishedinDecemberof1911.Thepoemspeaksaboutthewomen'slaborGustavsmiledwide.Hehasbeautifulwhitehairandasoftaccent().Hegrewupinmovement.Atthattime,conditionsinfactories,wheremanywomenworked,weredreadful.AfireatScandinaviaandisawoodfinisher.HiswifeVivianhasasmilethatfillstheirtinyhome.ShestoodaclothingfactoryinNewYorkkilled146people.awkwardly,andhaddifficultymovingabout.Itlookedterriblyuncomfortable.VivianhashadAmonthafterOppenheim'spoemwaspublished,womenworkersinLawrence,Massachusettsmusculardystrophy(肌肉菱缩)forover20years.Gustavisherfull---timecaregiver.They'vewentonwiththeirmarches,whichwonthemhigherpayandbetterworkingconditions.Oppenheim'sreplacedtheirdailywalkswithafternoondrives,buteventhosearegettingtoodifficultforVivian.poemreceivedmoreattention.GustavletKameronin,andViviantookholdofboththeirarmsandpulledtoherchair.On28.WhatdoesLaborDaymeantostudentsintheUnitedStates?thetablebesideherwasaphotoofherwithGustaywhentheywereyoungandenergetic,travelingA.It'stimetohaveapicnic.B.Theirsummervacationisover.aroundEurope,EgyptandIceland.Inthephoto,Vivianisverybeautiful,andGustavishandsome.C.ItteachesthemtorespectlaborD.Theycanlearnabouthistorythroughactivities.英语试题第3页（共8页）英语试题第4页（共8页）
分析（1）由解析式求出定义域和f′（x），化简后对k进行分类讨论，根据导数与函数单调性的关系，分别求出函数的增区间、减区间；
（2）由（1）求函数的最小值，由条件列出不等式求出k的范围，对k进行分类讨论，并分别判断在区间$（{1，\sqrt{e}}]$上的单调性，求出f（1）和f（$\sqrt{e}$）、判断出符号，即可证明结论．
解答解：（1）由$f（x）=\frac{{x}^{2}}{2}-klnx$得，函数的定义域是（0，+∞），
$f′（x）=x-\frac{k}{x}$=$\frac{{x}^{2}-k}{x}$；
①当k≤0时，f′（x）＞0，所以f（x）在（0，+∞）上单调递增，
此时f（x）的单调递增区间为（0，+∞），无单调递减区间；
②当k＞0时，由f′（x）=0得x=$\sqrt{k}$或x=-$\sqrt{k}$（舍去），
当$x＞\sqrt{k}$时，f′（x）＞0，
当$0＜x＜\sqrt{k}$时，令f′（x）＜0，
所以f（x）的递减区间是（0，$\sqrt{k}$），递增区间是（$\sqrt{k}，+∞$）；…（6分）
证明：（2）由（1）知，当k＞0时，f（x）在（0，+∞）上的最小值为
f（$\sqrt{k}$）=$\frac{k}{2}-k•ln\sqrt{k}$=$\frac{k（1-lnk）}{2}$．
因为f（x）存在零点，所以$\frac{k（1-lnk）}{2}≤0$，解得k≥e．
当k=e时，f（x）在（1，$\sqrt{e}$）上递减，且f（$\sqrt{e}$）=0，
所以x=$\sqrt{e}$是f（x）在（1，$\sqrt{e}$]上的唯一零点．
当k＞e时，f（x）在（0，$\sqrt{e}$）上单调递减，
且f（1）=$\frac{1}{2}＞$0，f（$\sqrt{e}$）=$\frac{e-k}{2}$＜0，
所以f（x）在区间（1，$\sqrt{e}$]上仅有一个零点．
综上可知，若f（x）存在零点，则f（x）在（1，$\sqrt{e}$]上仅有一个零点…（12分）
点评本题考查求导公式、法则，导数与函数单调性的关系，以及函数零点的转化，考查分类讨论思想，化简、变形能力，属于中档题．
